mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
347 lines
10 KiB
Python
347 lines
10 KiB
Python
|
{
|
||
|
|
"cells": [
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"# Solution Notebook"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Problem: Given a list of stock prices on each consecutive day, determine the max profits with k transactions.\n",
|
||
|
|
"\n",
|
||
|
|
"* [Constraints](#Constraints)\n",
|
||
|
|
"* [Test Cases](#Test-Cases)\n",
|
||
|
|
"* [Algorithm](#Algorithm)\n",
|
||
|
|
"* [Code](#Code)\n",
|
||
|
|
"* [Unit Test](#Unit-Test)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Constraints\n",
|
||
|
|
"\n",
|
||
|
|
"* Is k the number of sell transactions?\n",
|
||
|
|
" * Yes\n",
|
||
|
|
"* Can we assume the prices input is an array of ints?\n",
|
||
|
|
" * Yes\n",
|
||
|
|
"* Can we assume the inputs are valid?\n",
|
||
|
|
" * No\n",
|
||
|
|
"* If the prices are all decreasing and there is no opportunity to make a profit, do we just return 0?\n",
|
||
|
|
" * Yes\n",
|
||
|
|
"* Should the output be the max profit and days to buy and sell?\n",
|
||
|
|
" * Yes\n",
|
||
|
|
"* Can we assume this fits memory?\n",
|
||
|
|
" * Yes"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Test Cases\n",
|
||
|
|
"\n",
|
||
|
|
"<pre>\n",
|
||
|
|
"* Prices: None or k: None -> None\n",
|
||
|
|
"* Prices: [] or k <= 0 -> []\n",
|
||
|
|
"* Prices: [0, -1, -2, -3, -4, -5]\n",
|
||
|
|
" * (max profit, list of transactions)\n",
|
||
|
|
" * (0, [])\n",
|
||
|
|
"* Prices: [2, 5, 7, 1, 4, 3, 1, 3] k: 3\n",
|
||
|
|
" * (max profit, list of transactions)\n",
|
||
|
|
" * (10, [Type.SELL day: 7 price: 3, \n",
|
||
|
|
" Type.BUY day: 6 price: 1, \n",
|
||
|
|
" Type.SELL day: 4 price: 4, \n",
|
||
|
|
" Type.BUY day: 3 price: 1, \n",
|
||
|
|
" Type.SELL day: 2 price: 7, \n",
|
||
|
|
" Type.BUY day: 0 price: 2])\n",
|
||
|
|
"</pre>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Algorithm\n",
|
||
|
|
"\n",
|
||
|
|
"We'll use bottom up dynamic programming to build a table.\n",
|
||
|
|
"\n",
|
||
|
|
"<pre>\n",
|
||
|
|
"\n",
|
||
|
|
"The rows (i) represent the prices.\n",
|
||
|
|
"The columns (j) represent the number of transactions (k).\n",
|
||
|
|
"\n",
|
||
|
|
"T[i][j] = max(T[i][j - 1],\n",
|
||
|
|
" prices[j] - price[m] + T[i - 1][m])\n",
|
||
|
|
"\n",
|
||
|
|
"m = 0...j-1\n",
|
||
|
|
"\n",
|
||
|
|
" 0 1 2 3 4 5 6 7\n",
|
||
|
|
"--------------------------------------\n",
|
||
|
|
"| | 2 | 5 | 7 | 1 | 4 | 3 | 1 | 3 |\n",
|
||
|
|
"--------------------------------------\n",
|
||
|
|
"| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |\n",
|
||
|
|
"| 1 | 0 | 3 | 5 | 5 | 5 | 5 | 5 | 5 |\n",
|
||
|
|
"| 2 | 0 | 3 | 5 | 5 | 8 | 8 | 8 | 8 |\n",
|
||
|
|
"| 3 | 0 | 3 | 5 | 5 | 8 | 8 | 8 | 10 |\n",
|
||
|
|
"--------------------------------------\n",
|
||
|
|
"\n",
|
||
|
|
"Optimization:\n",
|
||
|
|
"\n",
|
||
|
|
"max_diff = max(max_diff,\n",
|
||
|
|
" T[i - 1][j - 1] - prices[j - 1])\n",
|
||
|
|
"\n",
|
||
|
|
"T[i][j] = max(T[i][j - 1],\n",
|
||
|
|
" prices[j] + max_diff)\n",
|
||
|
|
"\n",
|
||
|
|
"</pre>\n",
|
||
|
|
"\n",
|
||
|
|
"Complexity:\n",
|
||
|
|
"* Time: O(n * k)\n",
|
||
|
|
"* Space: O(n * k)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Code"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 1,
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": false
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"from enum import Enum # Python 2 users: Run pip install enum34\n",
|
||
|
|
"\n",
|
||
|
|
"\n",
|
||
|
|
"class Type(Enum):\n",
|
||
|
|
" SELL = 0\n",
|
||
|
|
" BUY = 1\n",
|
||
|
|
"\n",
|
||
|
|
"\n",
|
||
|
|
"class Transaction(object):\n",
|
||
|
|
"\n",
|
||
|
|
" def __init__(self, type, day, price):\n",
|
||
|
|
" self.type = type\n",
|
||
|
|
" self.day = day\n",
|
||
|
|
" self.price = price\n",
|
||
|
|
"\n",
|
||
|
|
" def __eq__(self, other):\n",
|
||
|
|
" return self.type == other.type and \\\n",
|
||
|
|
" self.day == other.day and \\\n",
|
||
|
|
" self.price == other.price\n",
|
||
|
|
"\n",
|
||
|
|
" def __repr__(self):\n",
|
||
|
|
" return str(self.type) + ' day: ' + \\\n",
|
||
|
|
" str(self.day) + ' price: ' + \\\n",
|
||
|
|
" str(self.price)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 2,
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": false
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"import sys\n",
|
||
|
|
"\n",
|
||
|
|
"\n",
|
||
|
|
"class StockTrader(object):\n",
|
||
|
|
"\n",
|
||
|
|
" def find_max_profit(self, prices, k):\n",
|
||
|
|
" if prices is None or k is None:\n",
|
||
|
|
" raise TypeError('prices or k cannot be None')\n",
|
||
|
|
" if not prices or k <= 0:\n",
|
||
|
|
" return []\n",
|
||
|
|
" num_rows = k + 1 # 0th transaction for dp table\n",
|
||
|
|
" num_cols = len(prices)\n",
|
||
|
|
" T = [[None] * num_cols for _ in range(num_rows)]\n",
|
||
|
|
" for i in range(num_rows):\n",
|
||
|
|
" for j in range(num_cols):\n",
|
||
|
|
" if i == 0 or j == 0:\n",
|
||
|
|
" T[i][j] = 0\n",
|
||
|
|
" continue\n",
|
||
|
|
" max_profit = -sys.maxsize\n",
|
||
|
|
" for m in range(j):\n",
|
||
|
|
" profit = prices[j] - prices[m] + T[i - 1][m]\n",
|
||
|
|
" if profit > max_profit:\n",
|
||
|
|
" max_profit = profit\n",
|
||
|
|
" T[i][j] = max(T[i][j - 1], max_profit)\n",
|
||
|
|
" return self._find_max_profit_transactions(T, prices)\n",
|
||
|
|
"\n",
|
||
|
|
" def find_max_profit_optimized(self, prices, k):\n",
|
||
|
|
" if prices is None or k is None:\n",
|
||
|
|
" raise TypeError('prices or k cannot be None')\n",
|
||
|
|
" if not prices or k <= 0:\n",
|
||
|
|
" return []\n",
|
||
|
|
" num_rows = k + 1\n",
|
||
|
|
" num_cols = len(prices)\n",
|
||
|
|
" T = [[None] * num_cols for _ in range(num_rows)]\n",
|
||
|
|
" for i in range(num_rows):\n",
|
||
|
|
" max_diff = prices[0] * -1\n",
|
||
|
|
" for j in range(num_cols):\n",
|
||
|
|
" if i == 0 or j == 0:\n",
|
||
|
|
" T[i][j] = 0\n",
|
||
|
|
" continue\n",
|
||
|
|
" max_diff = max(\n",
|
||
|
|
" max_diff,\n",
|
||
|
|
" T[i - 1][j - 1] - prices[j - 1])\n",
|
||
|
|
" T[i][j] = max(\n",
|
||
|
|
" T[i][j - 1],\n",
|
||
|
|
" prices[j] + max_diff)\n",
|
||
|
|
" return self._find_max_profit_transactions(T, prices)\n",
|
||
|
|
"\n",
|
||
|
|
" def _find_max_profit_transactions(self, T, prices):\n",
|
||
|
|
" results = []\n",
|
||
|
|
" i = len(T) - 1\n",
|
||
|
|
" j = len(T[0]) - 1\n",
|
||
|
|
" max_profit = T[i][j]\n",
|
||
|
|
" while i != 0 and j != 0:\n",
|
||
|
|
" if T[i][j] == T[i][j - 1]:\n",
|
||
|
|
" j -= 1\n",
|
||
|
|
" else:\n",
|
||
|
|
" sell_price = prices[j]\n",
|
||
|
|
" results.append(Transaction(Type.SELL, j, sell_price))\n",
|
||
|
|
" profit = T[i][j] - T[i - 1][j - 1]\n",
|
||
|
|
" i -= 1\n",
|
||
|
|
" j -= 1\n",
|
||
|
|
" for m in range(j + 1)[::-1]:\n",
|
||
|
|
" if sell_price - prices[m] == profit:\n",
|
||
|
|
" results.append(Transaction(Type.BUY, m, prices[m]))\n",
|
||
|
|
" break\n",
|
||
|
|
" return (max_profit, results)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Unit Test"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 3,
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": false
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Overwriting test_max_profit.py\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"%%writefile test_max_profit.py\n",
|
||
|
|
"from nose.tools import assert_equal\n",
|
||
|
|
"from nose.tools import assert_raises\n",
|
||
|
|
"from nose.tools import assert_true\n",
|
||
|
|
"\n",
|
||
|
|
"\n",
|
||
|
|
"class TestMaxProfit(object):\n",
|
||
|
|
"\n",
|
||
|
|
" def test_max_profit(self):\n",
|
||
|
|
" stock_trader = StockTrader()\n",
|
||
|
|
" assert_raises(TypeError, stock_trader.find_max_profit, None, None)\n",
|
||
|
|
" assert_equal(stock_trader.find_max_profit(prices=[], k=0), [])\n",
|
||
|
|
" prices = [5, 4, 3, 2, 1]\n",
|
||
|
|
" k = 3\n",
|
||
|
|
" assert_equal(stock_trader.find_max_profit(prices, k), (0, []))\n",
|
||
|
|
" prices = [2, 5, 7, 1, 4, 3, 1, 3]\n",
|
||
|
|
" profit, transactions = stock_trader.find_max_profit(prices, k)\n",
|
||
|
|
" assert_equal(profit, 10)\n",
|
||
|
|
" assert_true(Transaction(Type.SELL,\n",
|
||
|
|
" day=7,\n",
|
||
|
|
" price=3) in transactions)\n",
|
||
|
|
" assert_true(Transaction(Type.BUY,\n",
|
||
|
|
" day=6,\n",
|
||
|
|
" price=1) in transactions)\n",
|
||
|
|
" assert_true(Transaction(Type.SELL,\n",
|
||
|
|
" day=4,\n",
|
||
|
|
" price=4) in transactions)\n",
|
||
|
|
" assert_true(Transaction(Type.BUY,\n",
|
||
|
|
" day=3,\n",
|
||
|
|
" price=1) in transactions)\n",
|
||
|
|
" assert_true(Transaction(Type.SELL,\n",
|
||
|
|
" day=2,\n",
|
||
|
|
" price=7) in transactions)\n",
|
||
|
|
" assert_true(Transaction(Type.BUY,\n",
|
||
|
|
" day=0,\n",
|
||
|
|
" price=2) in transactions)\n",
|
||
|
|
" print('Success: test_max_profit')\n",
|
||
|
|
"\n",
|
||
|
|
"\n",
|
||
|
|
"def main():\n",
|
||
|
|
" test = TestMaxProfit()\n",
|
||
|
|
" test.test_max_profit()\n",
|
||
|
|
"\n",
|
||
|
|
"\n",
|
||
|
|
"if __name__ == '__main__':\n",
|
||
|
|
" main()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 4,
|
||
|
|
"metadata": {
|
||
|
|
"collapsed": false
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Success: test_max_profit\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"%run -i test_max_profit.py"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Python 3",
|
||
|
|
"language": "python",
|
||
|
|
"name": "python3"
|
||
|
|
},
|
||
|
|
"language_info": {
|
||
|
|
"codemirror_mode": {
|
||
|
|
"name": "ipython",
|
||
|
|
"version": 3
|
||
|
|
},
|
||
|
|
"file_extension": ".py",
|
||
|
|
"mimetype": "text/x-python",
|
||
|
|
"name": "python",
|
||
|
|
"nbconvert_exporter": "python",
|
||
|
|
"pygments_lexer": "ipython3",
|
||
|
|
"version": "3.4.3"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 0
|
||
|
|
}
|